Finite Group Databasebeta

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C11×C7⋊(C9⋊#261) #49114473

order36036
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C7⋊(C9⋊#261)
unambiguous semidirect productC7⋊(C11×C9⋊#261)
unambiguous semidirect productC9⋊(C11×C7⋊#261)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C4
derived, HallC7×C9×C13 ⋊ C4×C11
HallC9×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ Dic9
HallC7×C9×C11 ⋊ #261
HallC11×C13 ⋊ Dic63
HallC9×C13 ⋊ C11×Dic7
HallC9×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C11×Dic9
HallC7×C11 ⋊ C9⋊#261
HallC7×C9 ⋊ C11×#261
SylowC13 ⋊ C11×Dic63
SylowC9 ⋊ C11×C7⋊#261
SylowC7 ⋊ C11×C9⋊#261

Subgroups

subgroupG/H
center, hypercenterC11C7⋊(C9⋊#261)
commutator, hypocenterC7×C9×C13C4×C11
FrattiniC3C11×C3⋊(C7⋊#261)
FittingC7×C9×C11×C13C4
socleC3×C7×C11×C13Dic3
prime radicalC3×C7×C11×D13D3
cosocleC7×C9×D13C2×C11
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 141);